How do you expand log_3((uv^2)/w)?

1 Answer
Tony B
May 17, 2016

So log_3((uv^2)/w) -> (log_3(u)+2log_3(v))/log_3(w)

Explanation:

If source values are multiplied the logs are added
" " log(ab) -> log(a)+log(b)

Is source values are divided the logs are subtracted.
" "log(a/b)->log(a)-log(b)

If source values are raised to some power then the log is multiplied by the value of the power
" "log(a^4)->4log(a)

If source value are rooted then the log is divided by the value of that root
" "log(root(5)(a))-> 1/5log(a)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So log_3((uv^2)/w) -> (log_3(u)+2log_3(v))/log_3(w)

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